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LieAlgebras[MatrixCentralizer] - find the matrix centralizer of a list of matrices
Calling Sequences
MatrixCentralizer(M)
Parameters
M - a list of square matrices, each of the same dimension
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Description
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The centralizer of a set of matrices M is the Lie algebra of matrices which commute with all the matrices in M.
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A list of vectors defining a basis for the centralizer of M is returned.
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The command MatrixCentralizer is part of the DifferentialGeometry:-LieAlgebras package. It can be used in the form MatrixCentralizer(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-MatrixCentralizer(...).
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Examples
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Example 1.
Find the Matrix centralizer of the set of matrices M1.
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![M1 := [Matrix([[0, 1], [0, 0]])]](/support/helpjp/helpview.aspx?si=6622/file05815/math54.png)
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![M1 := [Matrix([[0, 1], [0, 0]])]](/support/helpjp/helpview.aspx?si=6622/file05815/math57.png)
| (2.1) |
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![[Matrix([[1, 0], [0, 1]]), Matrix([[0, 1], [0, 0]])]](/support/helpjp/helpview.aspx?si=6622/file05815/math64.png)
| (2.2) |
Example 2.
Find the Matrix centralizer of the set of matrices M2.
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![M2 := map(Matrix, [[[0, 0, 1], [0, 0, 0], [0, 0, 0]], [[0, 0, 1], [0, 0, 1], [0, 0, 0]], [[-1, -1, 0], [0, -1, 0], [0, 0, 0]]])](/support/helpjp/helpview.aspx?si=6622/file05815/math76.png)
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![M2 := [Matrix([[0, 0, 1], [0, 0, 0], [0, 0, 0]]), Matrix([[0, 0, 1], [0, 0, 1], [0, 0, 0]]), Matrix([[-1, -1, 0], [0, -1, 0], [0, 0, 0]])]](/support/helpjp/helpview.aspx?si=6622/file05815/math79.png)
| (2.3) |
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![[Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])]](/support/helpjp/helpview.aspx?si=6622/file05815/math86.png)
| (2.4) |
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